This dissertation documents my mathematical and computational models of the charging of spherical dust grains in plasmas. The mathematical models are stochastic models which predict the equilibrium probability distribution of a sphere's charge state q in a collisionless, flowing plasma with Debye length λ_D. I solve the models for the distribution's exact form and deduce closed-form Gaussian approximations to it. The approximations' mean and variance are of order Ω at large Ω, where the dimensionless quantity Ω equals 3 N_D a / λ_D, N_D being the plasma's Debye number and a the sphere's radius. Faster plasma flow increases q's variance for spheres much smaller than λ_D, but does not affect the variance for large (a >> λ_D) spheres. My computational model is pot, a simulator of a sphere in a flowing, homogeneously magnetized plasma, and the first to be fully microscopic with non-interpolated fields. I describe pot's design, present test results confirming that pot produces sensible output, and detail pot-derived estimates of a sphere's normalized, equilibrium surface potential η_a as a function of the dimensionless magnetization β_i and plasma flow speed. pot's η_a values come within 5% of those predicted by the existing "SOML" theory of spheres in flowing plasmas, and q's equilibrium fluctuations during pot simulations statistically match those predicted by my stochastic modelling. Another comparison, of pot's results against past simulations - only partially microscopic - and against an unmagnetized-ion theory, verifies the earlier simulations' implication that the unmagnetized-ion theory is incorrect when β_i is small but non-negligible. Contra the theory, gently magnetizing a proton-electron plasma by increasing its β_i from zero to 0.4 does not raise η_a by 0.4, but at most by 0.1.